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In mathematics, a matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix ''A'' is diagonally dominant if : where ''a''''ij'' denotes the entry in the ''i''th row and ''j''th column. Note that this definition uses a weak inequality, and is therefore sometimes called ''weak diagonal dominance''. If a strict inequality (>) is used, this is called ''strict diagonal dominance''. The unqualified term ''diagonal dominance'' can mean both strict and weak diagonal dominance, depending on the context.〔For instance, Horn and Johnson (1985, p. 349) use it to mean weak diagonal dominance.〕 ==Variations== The definition in the first paragraph sums entries across rows. It is therefore sometimes called ''row diagonal dominance''. If one changes the definition to sum down columns, this is called ''column diagonal dominance''. If an irreducible matrix is weakly diagonally dominant, but in at least one row (or column) is strictly diagonally dominant, then the matrix is ''irreducibly diagonally dominant''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Diagonally dominant matrix」の詳細全文を読む スポンサード リンク
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